what correlation might there be with the evolution of small population of a species on an isolated island?

Answer 1

The question doesn't make sense. A correlation is a relationship between two things. You mentioned one (the evolution of a small population).

Answer 2

I assume you mean 2 species ..

'small island' implies that will compete for the same resources and experience the same environment.

From a given starting position, multiple evolutionary paths suggest themselves - for example faster , heavier, more aggressive, more defensive etc. HOWEVER in the long term the only species to survive are those that find a 'niche' and thus avoid competing with other species for the same food resources.

The result will be multiple non-overlapping higher specialised species adapted to make use of single unique resources. See Darwin, Galapagos Islands